共查询到20条相似文献,搜索用时 415 毫秒
1.
We consider the (scalar) gradient fields η
a
= (η
b
)—with b denoting the nearest-neighbor edges in —that are distributed according to the Gibbs measure proportional to . Here H = ∑
b
V(η
b
) is the Hamiltonian, V is a symmetric potential, β > 0 is the inverse temperature, and ν is the Lebesgue measure on the linear space defined by
imposing the loop condition for each plaquette (b
1,b
2,b
3,b
4) in . For convex V, Funaki and Spohn have shown that ergodic infinite-volume Gibbs measures are characterized by their tilt. We describe a mechanism
by which the gradient Gibbs measures with non-convex V undergo a structural, order-disorder phase transition at some intermediate value of inverse temperature β. At the transition
point, there are at least two distinct gradient measures with zero tilt, i.e., E η
b
= 0. 相似文献
2.
LetN be a finite set. By a closure space we mean the family of the closed sets of a closure operator on 2
N
satisfying the additional condition
. A simple game on a closure space
is a functionv:
such that
andv (N)=1. We assume simple games are monotonic. The coalitions are the closed sets of
and the players are the elementsi∈N. We will give results concerning the structure of the core and the Weber set for this type of games. We show that a simple
game is supermodular if and only if the game is a unanimity game and theCore (
,v) is a stable set if and only if the gamev is a unanimity game.
This work was supported by the project USE 97-191 of the University of Seville. 相似文献
3.
The concept of evolutionarily stable strategies (ESS) has been central to applications of game theory in evolutionary biology, and it has also had an influence on the modern
development of game theory. A regular ESS is an important refinement the ESS concept. Although there is a substantial literature on computing evolutionarily stable
strategies, the precise computational complexity of determining the existence of an ESS in a symmetric two-player strategic
form game has remained open, though it has been speculated that the problem is -hard. In this paper we show that determining the existence of an ESS is both -hard and -hard, and that the problem is contained in , the second level of the polynomial time hierarchy. We also show that determining the existence of a regular ESS is indeed
-complete. Our upper bounds also yield algorithms for computing a (regular) ESS, if one exists, with the same complexities. 相似文献
4.
Jukka Lempa 《Applied Mathematics and Optimization》2012,65(2):147-173
We present a discrete n-person model of a dynamic strategic market game. We show that for some values of the discount factor the game possesses a
stationary equilibrium where all the players make high bids. Within the class of all the high-bidding strategies we distinguish
between two classes of more and less aggressive ones. We show that the set of discount factors for which these more aggressive
strategies form equilibria shrinks as n goes to infinity. On the other hand, the analogous set for the less aggressive strategies grows to the whole interval (0,1)
as n grows to infinity. Further we analyze the properties of the value function corresponding to these high-bidding equilibria.
We also give some numerical examples contradicting some other properties that seem intuitive. 相似文献
5.
Marc Kesseböhmer Manuel Stadlbauer Bernd O. Stratmann 《Mathematische Zeitschrift》2007,256(4):871-893
We study relations between (H,β)-KMS states on Cuntz-Krieger algebras and the dual of the Perron-Frobenius operator . Generalising the well-studied purely hyperbolic situation, we obtain under mild conditions that for an expansive dynamical
system there is a one-one correspondence between (H,β)-KMS states and eigenmeasures of for the eigenvalue 1. We then apply these general results to study multifractal decompositions of limit sets of essentially
free Kleinian groups G which may have parabolic elements. We show that for the Cuntz-Krieger algebra arising from G there exists an analytic family of KMS states induced by the Lyapunov spectrum of the analogue of the Bowen-Series map associated
with G. Furthermore, we obtain a formula for the Hausdorff dimensions of the restrictions of these KMS states to the set of continuous
functions on the limit set of G. If G has no parabolic elements, then this formula can be interpreted as the singularity spectrum of the measure of maximal entropy
associated with G.
The second author was supported by the DFG project “Ergodentheoretische Methoden in der hyperbolischen Geometrie”. 相似文献
6.
Joseph Y. Halpern 《International Journal of Game Theory》2009,38(1):37-49
New characterizations of sequential equilibrium, perfect equilibrium, and proper equilibrium are provided that use nonstandard
probability. It is shown that there exists a belief system μ such that is a sequential equilibrium in an extensive game with perfect recall iff there exist an infinitesimal and a completely mixed behavioral strategy profile σ′ (so that assigns positive, although possibly infinitesimal, probability to all actions at every information set) that differs only
infinitesimally from such that at each information set I for player i, σ
i
is an -best response to conditional on having reached I. Note that the characterization of sequential equilibrium does not involve belief systems. There is a similar characterization
of perfect equilibrium; the only difference is that σ
i
must be a best response to conditional on having reached I. Yet another variant is used to characterize proper equilibrium.
This work was supported in part by NSF under grants CTC-0208535, ITR-0325453, and IIS-0534064, and by AFOSR under grant FA9550-05-1-0055. 相似文献
7.
Jörg Eschmeier 《Archiv der Mathematik》2009,92(5):461-475
We use a variant of Grothendieck’s comparison theorem to show that, for a Fredholm tuple T ∈ L(X)n on a complex Banach space, there are isomorphisms . We conclude that a Fredholm tuple T ∈ L(X)n satisfies Bishop’s property (β) at z = 0 if and only if the vanishing conditions hold for . We apply these observations and results from commutative algebra to show that a graded tuple on a Hilbert space is Fredholm if and only if it satisfies Bishop’s property (β) at z = 0 and that, in this case, its cohomology groups can grow at most like kp.
Received: 14 January 2009 相似文献
8.
We study the semiflow defined by a semilinear parabolic equation with a singular square potential . It is known that the Hardy-Poincaré inequality and its improved versions, have a prominent role on the definition of the
natural phase space. Our study concerns the case 0 < μ ≤ μ*, where μ* is the optimal constant for the Hardy-Poincaré inequality. On a bounded domain of , we justify the global bifurcation of nontrivial equilibrium solutions for a reaction term f(s) = λs − |s|2γ
s, with λ as a bifurcation parameter. We remark some qualitative differences of the branches in the subcritical case μ < μ* and the critical case μ = μ*. The global bifurcation result is used to show that any solution , initiating form initial data tends to the unique nonnegative equilibrium. 相似文献
9.
We prove that two unital dual operator algebras A, B are stably isomorphic if and only if they are Δ-equivalent (Eleftherakis in J Pure Appl Algebra, ArXiv:math. OA/0607489v4,
2007), if and only if they have completely isometric normal representations α,β on Hilbert spaces H, K respectively and there exists a ternary ring of operators such that and
This project is cofunded by European Social Fund and National Resources—(EPEAEK II) “Pyhtagoras II” grant No. 70/3/7997. 相似文献
10.
Raúl E. Curto Lawrence A. Fialkow H. Michael Möller 《Integral Equations and Operator Theory》2008,60(2):177-200
For a degree 2n real d-dimensional multisequence to have a representing measure μ, it is necessary for the associated moment matrix to be positive semidefinite and for the algebraic variety associated to β, , to satisfy rank card as well as the following consistency condition: if a polynomial vanishes on , then . We prove that for the extremal case , positivity of and consistency are sufficient for the existence of a (unique, rank -atomic) representing measure. We also show that in the preceding result, consistency cannot always be replaced by recursiveness
of .
The first-named author’s research was partially supported by NSF Research Grants DMS-0099357 and DMS-0400741. The second-named
author’s research was partially supported by NSF Research Grant DMS-0201430 and DMS-0457138. 相似文献
11.
Mohammad Ghomi 《Geometriae Dedicata》2007,127(1):19-35
We prove that curves of constant curvature satisfy, in the sense of Gromov, the relative -dense h-principle in the space of immersed curves in Euclidean space R
n ≥ 3. In particular, in the isotopy class of any given knot f there exists a knot f͂ of constant curvature which is -close to f. More importantly, we show that if f is , then the curvature of f͂ may be set equal to any constant c which is not smaller than the maximum curvature of f. We may also require that f͂ be tangent to f along any finite set of prescribed points, and coincide with f over any compact set with an open neighborhood where f has constant curvature c. The proof involves some basic convexity theory, and a sharp estimate for the position of the average value of a parameterized
curve within its convex hull.
The author’s research was supported in part by NSF CAREER award DMS-0332333. 相似文献
12.
We introduce a renormalization procedure which allows us to study in a unified and concise way different properties of the
irrational rotations on the unit circle , . In particular, we obtain sharp results for the diffusion of the walk on generated by the location of points of the sequence {n
α + β} on a binary partition of the unit interval. Finally, we give some applications of our method.
相似文献
13.
Let κ be a cardinal which is measurable after generically adding many Cohen subsets to κ and let be the κ-Rado graph. We prove, for 2 ≤ m < ω, that there is a finite value such that the set [κ]
m
can be partitioned into classes such that for any coloring of any of the classes C
i
in fewer than κ colors, there is a copy of in such that is monochromatic. It follows that , that is, for any coloring of with fewer than κ colors there is a copy of such that has at most colors. On the other hand, we show that there are colorings of such that if is any copy of then for all , and hence . We characterize as the cardinality of a certain finite set of types and obtain an upper and a lower bound on its value. In particular, and for m > 2 we have where r
m
is the corresponding number of types for the countable Rado graph.
Research of M. Džamonja and J. A. Larson were partially supported by Engineering and Physical Sciences Research Council and
research of W. J. Mitchell was partly supported by grant number DMS 0400954 from the United States National Science Foundation. 相似文献
14.
Thomas Bartsch Shuangjie Peng Zhitao Zhang 《Calculus of Variations and Partial Differential Equations》2007,30(1):113-136
We investigate elliptic equations related to the Caffarelli–Kohn–Nirenberg inequalities: and such that . For various parameters α, β and various domains Ω, we establish some existence and non-existence results of solutions in
rather general, possibly degenerate or singular settings. 相似文献
15.
Julia Robinson gave a first-order definition of the set of integers in the rational numbers by a formula (∀∃∀∃)(F = 0) where the ∀-quantifiers run over a total of 8 variables and F is polynomial. We show that for a large class of number fields, not including , for every ε > 0 there exist a set of primes of natural density exceeding 1 − ε such that can be defined as a subset of the “large” subring
of K by a formula where there is only one ∀-quantifier. In the case of , we will need two quantifiers. We also show that in some cases one can define a subfield of a number field using just one
universal quantifier. Bibliography: 18 titles.
Dedicated to Yuri Matiyasevich on the occasion o his 60th birthday.
... the undecidable poem
“B Петербрге мы сойдемся снова” ... ([18])
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 358, 2008, pp. 199–223. 相似文献
16.
Using the methods of moving frames and exterior differential systems, we show that there exist Hopf hypersurfaces in complex
hyperbolic space with any specified value of the Hopf principal curvature α less than or equal to the corresponding value for the horosphere. We give a construction for all such hypersurfaces in terms
of Weierstrass-type data, and also obtain a classification of pseudo-Einstein hypersurfaces in .
相似文献
17.
For a nonempty compact set we determine the maximal possible dimension of a subspace of polynomial functions over Ω with degree at most m which possesses a positive basis. The exact value of this maximum depends on topological features of Ω, and we will see that in many of the cases m can be achieved. Whereas only for low m or finite sets Ω it is possible that we have a subspace X with positive basis and with dim X = m + 1. Hence there is no Ω for which a positive basis exists in for all .
This work was accomplished during the 2nd author’s stay in Paris under his Marie Curie fellowship, contract # MEIF-CT-2005-022927. 相似文献
18.
Yves Benoist 《Geometriae Dedicata》2006,122(1):109-134
For any m ≥ 3, we construct properly convex open sets Ω in the real projective space
whose Hilbert metric is Gromov hyperbolic but is not quasiisometric to the hyperbolic space
. We show that such examples cannot exist for m = 2.
Some of our examples are divisible, i.e. there exists a discrete group Г of projective transformations preserving Ω with a
compact quotient Г\Ω. The open set Ω is strictly convex but the group Г is not isomorphic to any cocompact lattice in the
isometry group of
. 相似文献
19.
J. Bourgain 《Israel Journal of Mathematics》2009,172(1):61-74
Distributional properties of small multiplicative subgroups of are obtained. In particular, it is shown that if H < is of size larger than polylogarithmic in p, then, letting β < 1 be a fixed exponent, most elements of any coset aH (a ∈ , arbitrary) will not fall into the interval [−p
β, p
β] ∈ . The arguments are based on the theory of heights and results from additive combinatoric. 相似文献
20.
Multipliers and Cyclic Vectors in Bloch Type Spaces 总被引:6,自引:0,他引:6
In this paper we study the coefficient multipliers, pointwise multipliers and cyclic vectors in the Bloch type spaces B
α
and little Bloch type spaces
for 0 < α < ∞. We give several full characterizations of the coefficient multipliers (B
α
,B
β
) and
for 0 < α, β < ∞ and pointwise multipliers M(B
α
,B
β
) and
for 1 ≠ α, β ∈ (0,∞). We also obtain some properties of cyclic vectors for Bloch type spaces.
Dedicated to Professor Yu Zan HE on the occasion of his 65th birthday 相似文献